Bin Talal, the billionaire member of the Saudi Arabian royal family who runs the Kingdom Holding Co., said the fear comes from "what may happen with Iran and the possibility of closing the Hormuz Strait."

But Saudi Arabia has already said it will not let the price of oil, which closed Monday around $97 a barrel, go above $100, bin Talal said.

"We can use our leverage, our excess capacity to be sure to pump more [oil] if needed so it will not impact the consumer countries while they’re getting out of their recessions slowly but surely," the prince said.

As for Iran, he said it is important for the U.S. and other nations to put sanctions on the "renegade country" to force its government to negotiate. Issuing an ultimatum of war would push Iran to the "desperate move" of blocking the vital oil shipment waterway.

"I believe a solution is not impossible with them," bin Talal said of Iran. "A dialog is the best way to do it."

Prince Alwaleed: Saudis Won't Let Oil Top $100

In a live interview with CNBC's Maria Bartiromo, Saudi Prince Alwaleed Bin Talal Bin Abdualaziz Alsaud, Chairman of Kingdom Holding Company, talks about the price of oil and whether Iran might follow through with its threat to close to Straits of Hormuz.

But if the strait is blocked he believes the U.S. can reopen the strait "very quickly." He added he wants a "nuclear-free" region, which means Israel should give up its nuclear arsenal, too.

He said the European debt crisis is "pulling down the growth of the world economies" and it is important for the European Union countries to "get their house in order because this can't go on indefinitely." Greece leaving the EU would set a bad precedent, he added, and could lead to the disintegration of the euro.

The prince, Citigroup's biggest shareholder, said CEO Vikram Pandithas brought the bank "out of the wilderness" and expects the company to pay a dividend or buy back shares sometime this year, once it gets clearance from the Federal Reserve .

Bin Talal, also a major shareholder in News Corp.and Apple , said he recently invested $300 million in Twitter, saying the huge number of its users makes it a "force to be reckoned with." He hasn't invested in Facebook, he said, but "we never say no to anything."